Police are looking for a woman who was seen mumbling to herself before she allegedly pushed an unsuspecting man to his death in front of an oncoming No. 7 train at a Queens subway station Thursday evening, police said.

The man was standing on the northbound platform of the 40th Street and Queens Boulevard elevated train when police say the woman walked up behind him and pushed him onto the tracks. Witnesses told police the man had his back to the woman and didn't appear to notice her. No words were exchanged.

"She's sick. She's completely sick," said Mohammed Haghi, a friend of the victim, identified by rommates and sources as Sunado Sen, of India. "To think to do something like that? She's not normal."

Witnesses told police the female suspect had been walking back and forth on the platform and talking to herself before sitting down, alone, on a wooden bench near the north end of the walkway. When the train pulled into the station shortly after 8 p.m., the woman got up off the bench and pushed Sen, according to witness statements.

The suspect then fled the platform, running down a flight of stairs to the turnstile area and down a second flight to Queens Boulevard. It's unknown where she went from there. Police released surveillance video of her running onto the street.

"We can't say with certainty whether or not there was no contact at some other location or perhaps before they got into the station," said Police Commissioner Ray Kelly. "But the witness says there was no contact between the two of them while she observed them on the platform." 

"We're reasonably confident we'll be able to identify the perpetrator in this case," said Kelly. 

Sen, a native of Calcutta, had been in the country for more than 20 years and was part owner of New Amsterdam Printing on Amsterdam Avenue, according to his three roommates. Sen had opened the business six months ago and worked seven days a week, commuting by subway daily, his friends and roommates said. 

"He is so nice. Quiet and friendly," said MD Khan, one of Sen's roommates. 

The suspect is described as being a heavyset woman about 5 feet 5 inches tall with brown or blond hair. She was wearing a white and gray ski jacket and Nike sneakers at the time of the incident. A $10,000 reward was being offered for information leading to an arrest in the incident. 

Asked about the incident Friday on his radio show, Mayor Bloomberg pointed to legal and policy changes that led to the release of many mentally ill people from psychiatric institutions from the 1960s through 1990s.

"The courts or the law have changed and said, no, you can't do that unless they're a danger to society; our laws protect you. That's fair enough," Bloomberg said on "The John Gambling Show with Mayor Mike" on WOR-AM.

It is the second time this month that a person has been shoved onto subway train tracks and killed.

Naeem Davis, a 30-year-old deli worker, was recently arrested and charged with second-degree murder for allegedly pushing Ki-Suk Han, 58, off a midtown subway platform to his death on Dec. 3. Han was struck by a southbound Q train at the 49th Street station in Manhattan.

Riders on Friday said the second fatal push in a matter of weeks was unnerving.

Micah Siegel follows her own set of safety precautions during her daily commute: stand against a wall or pillar to keep someone from coming up behind you, watch out when navigating a crowded or narrow platform to avoid being knocked — even accidentally — onto the tracks.

"I do try to be aware of what's around me and who's around me, especially as a young woman," Siegel, a 21-year-old college student, said as she waited at Pennsylvania Station on Friday.

Bloomberg urged residents to keep the second fatal subway shove in the city this month in perspective. 

"I don't think you have to sit there and worry about getting pushed off the platform," he said. "It is such a rare occurrence. No matter how tragic it is, it shouldn't change our lifestyle."